As Corvaja–Zannier show in [1]}, the Hilbert property for varieties over number fields forces topological constraints on the variety.
Namely, if \(X\)  is a normal projective variety with the Hilbert property over a number field \(K\) , then each finite étale cover of \(X_{\overline{K}}\) 
is trivial, i.e., the étale fundamental group \(\pi _1^{\textrm {ét}}(X_{\overline{K}})\)  is trivial.
We follow very closely Corvaja–Zannier's line of reasoning and prove an analogue of their theorem in the setting of arithmetic schemes over regular finitely generated integral domains of characteristic zero.
